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Rewrite the following equation in standard form. $\newline$ $y = 10x + 7$ $\newline$ Hint: The standard form of a linear equation is $Ax + By = C$ where $A$ and $B$ are not both zero, and $A$ , $B$ , and $C$ are integers whose GCF is $1$ .

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Write linear equations in standard form

Full solution

Q. Rewrite the following equation in standard form.

\newline

y = 10x + 7

\newline

Hint: The standard form of a linear equation is

Ax + By = C

where

A

and

B

are not both zero, and

A

,

B

, and

C

are integers whose GCF is

1

.

Start Equation Rearrangement: Start with the given equation. $\newline$ $y = 10x - 7$ $\newline$ We need to rearrange this equation to the standard form, which is $Ax + By = C$ .
Move $x$ Term: Move the term involving $x$ to the other side of the equation by subtracting $10x$ from both sides. $\newline$ $y - 10x = -7$ $\newline$ This is not the standard form yet because the $x$ term should be before the $y$ term.
Rearrange Terms: Rearrange the terms to place the $x$ term first. $\newline$ $-10x + y = -7$
Make Coefficient Positive: Multiply the entire equation by $-1$ to make the coefficient of $x$ positive, as it is customary for the $A$ term in standard form to be positive. $\newline$ $(-1)(-10x) + (-1)y = (-1)(-7)$ $\newline$ $10x - y = 7$

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